Journal of Soviet Mathematics

, Volume 13, Issue 1, pp 1–23 | Cite as

Geometry of Lagrangian manifolds and the canonical Maslov operator in complex phase space

  • A. S. Mishchenko
  • B. Yu. Sternin
  • V. E. Shatalov


A number of geometric questions related to the complex theory of the canonical Maslov operator are considered. The investigations center around the following themes: 1) quantization conditions and the problem of finding the asymptotics of eigenvalues; 2) universal characteristics of the theory of the complex canonical operator; 3) complex Hamiltonian fields and their trajectories.


Manifold Phase Space Quantization Condition Complex Theory Complex Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    V. I. Arnol'd, “On the characteristic class contained in the quantization condition,” Funkts. Anal. Prilozhen.,1, No. 1, 1–14 (1967).Google Scholar
  2. 2.
    V. V. Kucherenko, “Asymptotic solutions of equations with complex characteristics,” Mat. Sb.,95, No. 2, 163–213 (1974).Google Scholar
  3. 3.
    V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], Moscow State Univ. (1965).Google Scholar
  4. 4.
    V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973).Google Scholar
  5. 5.
    A. S. Mishchenko and B. Yu. Sternin, The Method of the Canonical Operator in Applied Mathematics [in Russian], MIÉM, Moscow (1974).Google Scholar
  6. 6.
    A. S. Mishchenko, B. Yu. Sternin, and V. E. Shatalov, The Canonical Operator of Maslov. The Complex Theory [in Russian], MIÉM, Moscow (1974).Google Scholar
  7. 7.
    S. P. Novikov and B. Yu. Sternin, “Traces of elliptic operators on submanifolds and K-theory,” Dokl. Akad. Nauk SSSR,170, No. 6, 1265–1268 (1966).Google Scholar
  8. 8.
    S. P. Novikov and B. Yu. Sternin, “Elliptic operators and submanifolds,” Dokl. Akad. Nauk SSSR,171, No. 3, 525–528 (1966).Google Scholar
  9. 9.
    B. Yu. Sternin, “Elliptic (co)boundary morphisms,” Dokl. Akad. Nauk SSSR,172, No. 1, 44–47 (1967).Google Scholar
  10. 10.
    J. J. Duistermaat, Fourier Integral Operators, Courant Inst. Math., New York Univ. (1973).Google Scholar
  11. 11.
    L. Hörmander, “Fourier integral operators. I,” Acta Math., Nos. 1–2, 79–183 (1971).Google Scholar
  12. 12.
    A. Melin and J. Sjöstrand, “Fourier integrals with complex-valued phase functions,” Lect. Notes Math., No. 459, 120–223 (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • A. S. Mishchenko
  • B. Yu. Sternin
  • V. E. Shatalov

There are no affiliations available

Personalised recommendations